We consider the case where the viscous fluid is withdrawn such that as the interface contracts, viscous fingers form inward. As described in sec:complex, exact solutions in the absence of surface tension (\(\sigma = 0\) ) are ill-posed, and unphysical cusps can form before the interface reaches the sink (the point at which liquid is withdrawn). Numerical simulations performed using the boundary integral method have investigated the regularising effects of surface tension preventing these cusps from forming [1]}, [2]}. Experimental results [3]}, [4]} show that the fingers that form exhibit morphological features distinct from traditional Saffman–Taylor fingers, in that these fingers do not appear to undergo tip-splitting but instead appear to be in competition to `race' toward the sink.
